Keeping a lot of state in your head while modifying a program. "Don't bother me now, I'm juggling eggs", means that an interrupt is likely to result in the program's being scrambled. In the classic first-contact SF novel "The Mote in God's Eye", by Larry Niven and Jerry Pournelle, an alien describes a very difficult task by saying "We juggle priceless eggs in variable gravity." See also hack mode.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)